Nonlinear bending analysis of FGM circular plates based on physical neutral surface and higher-order shear deformation theory

Zhang, Da-Guang; Zhou, Hao-Miao

doi:10.1016/j.ast.2014.12.016

Cited by 38 publications

(7 citation statements)

References 47 publications

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“…The parameter 0 z which is the distance between the middle surface and physical neutral surface, was considered at a constant level in all of the previous works [41][42][43][44][45][46][47][48][49][50]. However, Eq.…”

Section: Equilibrium Equationsmentioning

confidence: 99%

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Geometrically non-linear bending analysis of thick two-directional functionally graded annular sector and rectangular plates with variable thickness resting on non-linear elastic foundation

Alinaghizadeh

Shariati

2016

Composites Part B: Engineering

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Section: Equilibrium Equationsmentioning

confidence: 99%

“…Owing to the merits of the concept of physical neutral surface, the interest in this concept is increasing [46][47][48][49][50]. According to latest review of open literature geometrically non-linear behaviors of multi-dimensional FGMs have not been studied based on the physical neutral surface.…”

Section: Introductionmentioning

confidence: 99%

Geometrically non-linear bending analysis of thick two-directional functionally graded annular sector and rectangular plates with variable thickness resting on non-linear elastic foundation

Alinaghizadeh

Shariati

2016

Composites Part B: Engineering

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“…since the introduction of neutral surface [39], B ij = 0. The forces and bending moments generated by the electric field can be calculated by…”

Section: Constitutive Relationshipmentioning

confidence: 99%

A Simple-FSDT-Based Isogeometric Method for Piezoelectric Functionally Graded Plates

Liu

Wang

et al. 2020

Mathematics

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An efficient isogeometric analysis method (IGA) based on a simple first-order shear deformation theory is presented to study free vibration, static bending response, dynamic response, and active control of functionally graded plates (FGPs) integrated with piezoelectric layers. Based on the neutral surface, isogeometric finite element motion equations of piezoelectric functionally graded plates (PFGPs) are derived using the linear piezoelectric constitutive equation and Hamilton’s principle. The convergence and accuracy of the method for PFGPs with various mechanical and electrical boundary conditions have been investigated via free vibration analysis. In the dynamic analysis, both time-varying mechanical and electrical loads are involved. A closed-loop control method, including displacement feedback control and velocity feedback control, is applied to the static bending control and the dynamic vibration control analysis. The numerical results obtained are accurate and reliable through comparisons with various numerical and analytical examples.

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“…e temperature dependence of the FGM should be considered in a thermal environment. Since Young's modulus E and thermal expansion coefficient α vary greatly with the temperature, while the Poisson ratio μ, material density ρ, and thermal conductivity κ generally are temperature independent, so only E and α in (13) are assumed to be related to the temperature and uniformly expressed by (Lal et al [20] and Zhang and Zhou [32])…”

Section: Physical Properties Of Fgmmentioning

confidence: 99%

“…Besides, the FG plate generally deforms largely when subjected to the combined action of thermomechanical loads, and its mechanical behavior is usually nonlinear in this situation. For the nonlinear mechanical problems of FG plates in thermal environment, some relevant works were summarized in [29][30][31][32]. All these works proved that solving mechanical problems by simple linearization cannot meet the precision requirement in important structural calculations.…”

Section: Introductionmentioning

confidence: 99%

A Spline Finite Point Method for Nonlinear Bending Analysis of FG Plates in Thermal Environments Based on a Locking-free Thin/Thick Plate Theory

Huang

et al. 2020

Mathematical Problems in Engineering

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A spline finite point method (SFPM) based on a locking-free thin/thick plate theory, which is suitable for analysis of both thick and thin plates, is developed to study nonlinear bending behavior of functionally graded material (FGM) plates with different thickness in thermal environments. In the proposed method, one direction of the plate is discretized with a set of uniformly distributed spline nodes instead of meshes and the other direction is expressed with orthogonal functions determined by the boundary conditions. The displacements of the plate are constructed by the linear combination of orthogonal functions and cubic B-spline interpolation functions with high efficiency for modeling. The locking-free thin/thick plate theory used by the proposed method is based on the first-order shear deformation theory but takes the shear strains and displacements as basic unknowns. The material properties of the FG plate are assumed to vary along the thickness direction following the power function distribution. By comparing with several published research studies based on the finite element method (FEM), the correctness, efficiency, and generality of the new model are validated for rectangular plates. Moreover, uniform and nonlinear temperature rise conditions are discussed, respectively. The effect of the temperature distribution, in-plane temperature force, and elastic foundation on nonlinear bending under different parameters are discussed in detail.

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Nonlinear bending analysis of FGM circular plates based on physical neutral surface and higher-order shear deformation theory

Cited by 38 publications

References 47 publications

Geometrically non-linear bending analysis of thick two-directional functionally graded annular sector and rectangular plates with variable thickness resting on non-linear elastic foundation

Geometrically non-linear bending analysis of thick two-directional functionally graded annular sector and rectangular plates with variable thickness resting on non-linear elastic foundation

A Simple-FSDT-Based Isogeometric Method for Piezoelectric Functionally Graded Plates

A Spline Finite Point Method for Nonlinear Bending Analysis of FG Plates in Thermal Environments Based on a Locking-free Thin/Thick Plate Theory

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